- 14 Mar '06 01:33Nathan has an aunt Marie living 50 miles to his east and another aunt Clara living 50 miles to the west. Nathan lives close to the railway station and decides to visit one of his aunts every week. There are trains to both heading East and West ; the number of trains are equal in both the directions , in fact, equal numbers every hour,

Nathan decides to adopt a simple system which will also ensure that he does not have to waste time waiting in his station. He will go the station whenever he is free and take whatever train happens to come to the station next and go east bound to visit aunt Marie or west bound to visit aunt Clara. He figures that over a period of one year , this arrangement should work out all right .

To his amazement , at the end of the year, aunt Marie is very upset with him for being very mean and partial in his affections; her complaint was that he has been paying much larger number of visits to Clara. Well ,assuming that Clara does not have a beautiful daughter nor she cooks much better than Marie - What do you think has happened here? - 14 Mar '06 01:37In the court of "Hindiainfo" where many queer things happen, one day the king called his sage who was the teacher of his princes. He wanted to check the intelligence of the newly appointed teacher. So he called the sage and gave him the following task.

"You are given 4000 oranges and a dozen(12) baskets. The baskets are quite large and let us assume that there will be no problem of capacity and they can hold any number of oranges.

You need to distribute all the oranges in these 12 baskets after which the baskets will be sealed.

You should have placed the oranges among these 12 baskets in such a way that, no matter what number of oranges is demanded by me subsequently, you should give that many number of oranges in terms of baskets –i.e., you are not allowed to break up any basket. The number of oranges demanded may be 3789 or 121 or 2183 or any such number .You should hand over the oranges demanded in terms of a few or all baskets( in case 4000 is demanded)."

The sage, who was a very intelligent man, after a little thought agreed to do it and requested the king to provide him the oranges as well as those extraordinary baskets.

Will the sage be able to do it? Can you do it? How will you do it? - 14 Mar '06 01:43

Although there are equal numbers every hour, they are scheduled in a regular order, and Nathan tends to be free at the same time each week, and thus his trips to the train station coincide with the appearance of a westbound train more frequently than they do with an eastbound train.*Originally posted by flyUnity***Nathan has an aunt Marie living 50 miles to his east and another aunt Clara living 50 miles to the west. Nathan lives close to the railway station and decides to visit one of his aunts every week. There are trains to both heading East and West ; the number of trains are equal in both the directions , in fact, equal numbers every hour,**

Nathan decides to a ...[text shortened]... a beautiful daughter nor she cooks much better than Marie - What do you think has happened here?

A simple case of this would be if a train came every ten minutes, alternating east- and west- bound, such that westbound trains come on the hour and eastbound ones come at ten minutes to the hour. Nathan tends to be free at the beginnings of hours, and thus tends to get the westbound train. - 14 Mar '06 01:48 / 1 edit

Every positive integer is representable as the sum of powers of two, so the first eleven baskets hold 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 oranges each. This gets us any number up to 2047, so put 1953 in the last basket. This does the trick.*Originally posted by flyUnity***In the court of "Hindiainfo" where many queer things happen, one day the king called his sage who was the teacher of his princes. He wanted to check the intelligence of the newly appointed teacher. So he called the sage and gave him the following task.**

"You are given 4000 oranges and a dozen(12) baskets. The baskets are quite large and let us assume that extraordinary baskets.

Will the sage be able to do it? Can you do it? How will you do it? - 14 Mar '06 01:55

Fill the 3-gallon bucket.*Originally posted by flyUnity***Somone sends you to the river with 2 buckets, One holds exactly 3 gallons, the other holds 5 gallons, He instructs you to bring back exactly 4 gallons. you can only make one trip.**

How do you do this?

Pour it into the five-gallon bucket.

Do the same again. The 5-gallon bucket is now full and the three-gallon bucket contains one gallon. Dump out the 5-gallon bucket and pour the one gallon from the other bucket in. Fill the three gallon bucket, and pour it into the five-gallon bucket. This now contains 4 gallons. - 14 Mar '06 01:57

lol, Im surprised that your chess rating isnt higher then it is, or did you already hear these before?*Originally posted by royalchicken***Fill the 3-gallon bucket.**

Pour it into the five-gallon bucket.

Do the same again. The 5-gallon bucket is now full and the three-gallon bucket contains one gallon. Dump out the 5-gallon bucket and pour the one gallon from the other bucket in. Fill the three gallon bucket, and pour it into the five-gallon bucket. This now contains 4 gallons. - 14 Mar '06 01:59 / 1 edit

I'm a second-year maths undergraduate, I should be able to do this sort of thing.*Originally posted by flyUnity***lol, Im surprised that your chess rating isnt higher then it is, or did you already hear these before?**

I just sort of suck at chess, a state of affairs not helped by the fact that I've not read any books on the subject and never play OTB.

For something slightly harder, but basically contained in my solution:

In the oranges one, how many baskets are required for n oranges?